Question:  Find the equation of the tangent line to r = 1+cos(θ) at θ = π/6

Solution:

A polar curve is a shape constructed using the polar coordinate system. Polar curves are defined by points that are a variable distance from the origin (the pole) depending on the angle measured off the positive -axis. Polar curves can describe familiar Cartesian shapes such as ellipses as well as some unfamiliar shapes such as cardioids and lemniscates.

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Tangent line touching a Polar curve (a Cardioid)

                                                                                    

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